>> skript_u10
 
% Aufagbe 1
f = (x + 1)/y
f_x = 1/y
f_y = -(x + 1)/y^2
f_xx = 0
f_xy = -1/y^2
f_yy = (2*(x + 1))/y^3
 
 
f = x^3*sin(y)
f_x = 3*x^2*sin(y)
f_y = x^3*cos(y)
f_xx = 6*x*sin(y)
f_xy = 3*x^2*cos(y)
f_yy = -x^3*sin(y)
 
 
f = cos(x*y)*log(x + y)
f_x = cos(x*y)/(x + y) - y*log(x + y)*sin(x*y)
f_y = cos(x*y)/(x + y) - x*log(x + y)*sin(x*y)
f_xx = - cos(x*y)/(x + y)^2 - (2*y*sin(x*y))/(x + y) - y^2*cos(x*y)*log(x + y)
f_xy = - cos(x*y)/(x + y)^2 - log(x + y)*sin(x*y) - (x*sin(x*y))/(x + y) - (y*sin(x*y))/(x + y) - x*y*cos(x*y)*log(x + y)
f_yy = - cos(x*y)/(x + y)^2 - (2*x*sin(x*y))/(x + y) - x^2*cos(x*y)*log(x + y)
 
 
f = (x^2 + y)^(1/2)
f_x = x/(x^2 + y)^(1/2)
f_y = 1/(2*(x^2 + y)^(1/2))
f_xx = 1/(x^2 + y)^(1/2) - x^2/(x^2 + y)^(3/2)
f_xy = -x/(2*(x^2 + y)^(3/2))
f_yy = -1/(4*(x^2 + y)^(3/2))
 
 
f = (x^2 + y^2)/c
f_x = (2*x)/c
f_y = (2*y)/c
f_xx = 2/c
f_xy = 0
f_yy = 2/c
 

% Aufgabe 2 
f = x*y + y*sin(x)
df = dx*(y + y*cos(x)) + dy*(x + sin(x))
ddf = dx*dy*(2*cos(x) + 2) - dx^2*y*sin(x)
 
 
f = x^2 + 2*y*x - cos(y)
df = dx*(2*x + 2*y) + dy*(2*x + sin(y))
ddf = 2*dx^2 + 4*dx*dy + cos(y)*dy^2
 

% Aufgabe 3 
f = x^3 + y^3 + 2
f_x = 3*x^2
f_y = 3*y^2
y_x = -x^2/y^2
 
 
f = log(y) + x*y + y^2
f_x = y
f_y = x + 2*y + 1/y
y_x = -y/(x + 2*y + 1/y)
 
 
% Aufgabe 4
f = (p + a/V^2)*(V - b) - R*T
f_V = p + a/V^2 - (2*a*(V - b))/V^3
f_T = -R
V_T = (R*V^3)/(p*V^3 - a*V + 2*a*b)